Integrality of instanton numbers and p-adic B-model

Abstract

We study integrality of instanton numbers (genus zero Gopakumar–Vafa invariants) for quintic and other Calabi–Yau manifolds. We start with the analysis of the case when the moduli space of complex structures is one-dimensional; later we show that our methods can be used to prove integrality in general case. We give an expression of instanton numbers in terms of Frobenius map on p-adic cohomology; the proof of integrality is based on this expression.